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Examples 9 to 11

(9) Find the median of 15, 35, 42, 45, 18.

Soln. Writing them in ascending order : 15, 18, 35, 42, 45. Here, n = 5.

$\therefore$ M = $\left (\frac{n+1}{2} \right )^{th}$ observation = $\left (\frac{5+1}{2} \right ) ^{th}$ observation = 3^rd observation = 35.

(10) Find the median of 10, 15, 25, 45, 18, 12

Soln. Writing them in ascending order : 10, 12, 15, 18, 25, 45. Here, n = 6.

$\therefore$ M = $\left (\frac{n+1}{2} \right )^{th}$ observation = $\left (\frac{6+1}{2} \right ) ^{th}$ observation

= 3.5th observation = $\frac{3^{rd} obs. + 4^{th} obs.}{2}$ = $\frac{15 + 18 }{2}$ = 16.5

(11) Find the median of the following frequency distribution :

Marks	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
Number of Students	5	8	15	12	10

Soln.

Here, Median Class = The class in which $\left (\frac{n}{2} \right ) ^{th}$ observation lies

= The class in which 25^th observation lies

= 30 – 40

f = 15, C = 10

$\therefore L = 30 , cf=13.$